ALPHA DIVISION

Question 53

Trigonometry★★★Question Bank

Loading saved statistics and bookmark… You can read the question while this loads.

⏱ Time: 0:00

Question

Which of the following statements are true?

\begin{aligned} 1.&\ \text{For real }a,b,\ \cos^{-1}(a)<\cos^{-1}(b)\Rightarrow a<b.\\ 2.&\ \sin\!\left(2\cos^{-1}\!\frac35\right)=\frac{24}{25}.\\ 3.&\ \sin(\sin^{-1}x+\cos^{-1}x)=1\quad\text{for }-1\le x\le1.\\ 4.&\ \text{The range of }y=\tan^{-1}x\text{ is }\left[-\frac\pi2,\frac\pi2\right]. \end{aligned}

Loading practice…

Getting your questions ready.

Question

Which of the following statements are true?

\begin{aligned} 1.&\ \text{For real }a,b,\ \cos^{-1}(a)<\cos^{-1}(b)\Rightarrow a<b.\\ 2.&\ \sin\!\left(2\cos^{-1}\!\frac35\right)=\frac{24}{25}.\\ 3.&\ \sin(\sin^{-1}x+\cos^{-1}x)=1\quad\text{for }-1\le x\le1.\\ 4.&\ \text{The range of }y=\tan^{-1}x\text{ is }\left[-\frac\pi2,\frac\pi2\right]. \end{aligned}